An investigation of the maximum particle velocity as an invariant in acoustofluidic applications and more

Vibrating materials experience internal stress waves that can cause material failure or energy loss due to inelastic vibration. Failure is traditionally defined in terms of acceleration, yet this approach has many drawbacks, principally because it is not invariant with respect to scale, type of vibration, or material choice. Here, the likelihood of failure is instead defined in terms of the maximum particle velocity. While the exact dependence of the internal stress on the particle velocity may be determined for specific cases, here we take a statistical approach in seeking a universal maximum particle velocity correlated to a specific risk of material failure. Our Monte Carlo-based analysis on a variety of materials, vibration types and frequencies, structures with flaws, and vibration velocities produced results in support of the notion that a maximum particle velocity on the order of 1 m/s is a universal and critical limit. Upon exceeding this limit, we find the probability of failure or excessive acoustic loss in suppression of the vibration to become significant, regardless of the details of the material, geometry, or vibration. We illustrate this in a specific example relevant to acoustofluidics, a simple surface acoustic wave device with fluid sample, and point out the value of using the maximum particle velocity as a design invariant.